In "The Man in the High Castle", "travel" can only occur when a person is in a meditative state.
In the alt-history, Admiral Toshihira Inoguchi arrives in San Francisco on board the battleship Musashi, escorted by the aircraft carrier Taiho and an unidentified Mogami class heavy cruiser. In reality, then Captain Inoguchi died when the Musashi was sunk at the Battle of Leyte Gulf on October 24, 1944, the Taiho was sunk at the Battle of the Philippine Sea on June 19, 1944 and all four of the Mogami class were sunk between 1942 and 1944.
In Philip K. Dick's novel, Army Field Marshall Rommel becomes Reichsmarshall of America after the 1945 invasion. Rommel is primarily concerned with suppressing the Rebel American Army, which resulted in a negligent implementation of Hitler's Final Solution (complete extermination of the Jewish population). As a result, many Jewish and African Americans escaped to the Neutral Zone and the JPS during the last two years of the war.
In "The Man in the High Castle", the Reich controls Europe, Africa and the Middle East, so their control of mineral and oil resources is far vaster than that of the Japanese Empire, which controls India, Indonesia, Australia and a large part of China. They share North America.
The Nazis and the Japanese closely monitor what happens in the Neutral Zone, dispatching spies, informants and private contractors to hunt down Jews and wanted subversives.